Space of modular forms of level 775, weight 2, and Character 775.b

• Label: 775.2.b
• Level: $775$
• Weight: $2$
• Character orbit: 775.b
• Rep. character: $\chi_{775}(249,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $8$
• Sturm bound: $160$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(160\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(775, [\chi])\).

	Total	New	Old
Modular forms	86	46	40
Cusp forms	74	46	28
Eisenstein series	12	0	12

Trace form

46 * q - 48 * q^4 - 8 * q^6 - 34 * q^9 - 12 * q^11 + 2 * q^14 + 68 * q^16 - 8 * q^19 - 28 * q^21 + 28 * q^24 - 28 * q^26 + 16 * q^29 + 6 * q^31 - 52 * q^34 - 28 * q^36 - 4 * q^39 + 60 * q^44 + 20 * q^46 - 10 * q^49 - 36 * q^51 - 24 * q^59 + 12 * q^61 - 110 * q^64 - 4 * q^66 + 32 * q^69 - 16 * q^71 - 12 * q^74 - 22 * q^76 + 64 * q^79 + 22 * q^81 + 76 * q^84 - 64 * q^86 + 44 * q^89 - 72 * q^91 + 32 * q^94 - 52 * q^96 + 136 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
775.2.b.a	$775$	$2$	775.b	5.b	$2$	$2$	$2$	$6.188$	\(\Q(\sqrt{-1}) \)	None					155.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-i q^{3}-2 q^{4}+2 q^{6}+2 i q^{7}+\cdots\)
775.2.b.b	$775$	$2$	775.b	5.b	$2$	$2$	$2$	$6.188$	\(\Q(\sqrt{-1}) \)	None					155.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}+q^{4}-2 q^{6}-4 i q^{7}+\cdots\)
775.2.b.c	$775$	$2$	775.b	5.b	$2$	$2$	$2$	$6.188$	\(\Q(\sqrt{-1}) \)	None					155.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 q^{4}+2 q^{9}-4 q^{11}-2 i q^{12}+\cdots\)
775.2.b.d	$775$	$2$	775.b	5.b	$2$	$4$	$4$	$6.188$	\(\Q(i, \sqrt{5})\)	None					31.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+2\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots\)
775.2.b.e	$775$	$2$	775.b	5.b	$2$	$8$	$8$	$6.188$	8.0.\(\cdots\).1	None					155.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-2+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
775.2.b.f	$775$	$2$	775.b	5.b	$2$	$8$	$8$	$6.188$	8.0.4589249536.2	None					155.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{4})q^{4}+(-1+\cdots)q^{6}+\cdots\)
775.2.b.g	$775$	$2$	775.b	5.b	$2$	$10$	$10$	$6.188$	10.0.\(\cdots\).1	None		✓			775.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}+\beta _{7})q^{2}+(-\beta _{4}-\beta _{8})q^{3}+(-1+\cdots)q^{4}+\cdots\)
775.2.b.h	$775$	$2$	775.b	5.b	$2$	$10$	$10$	$6.188$	10.0.\(\cdots\).1	None		✓			775.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(-2+\beta _{6}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(775, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)